Size- and shape-dependent phase diagram of In-Sb nano-alloys

Abstract

Nano-scale alloy systems with at least one dimension below 100 nm have different phase stabilities than those observed in the macro-scale systems due to a large surface to volume ratio. We have used the semi-empirical thermodynamic modelling, i.e. the CALPHAD method, to predict the phase equilibria of the In-Sb nano-scale systems as a function of size and shape. To calculate the size- and shape-dependent phase diagram of the In-Sb system, we have added size-dependent surface energy terms to the Gibbs energy expressions in the In-Sb thermodynamic database. We estimated the surface energies of the solution phases and of the InSb intermetallic phase using the Butler equation and DFT calculations, respectively. A melting point and eutectic point depression were observed for both nanoparticle and nanowire systems. The eutectic composition on the In-rich and Sb-rich sides of the phase diagram shifted towards higher solubility. We believe that the phase diagram of In-Sb nano-alloys is useful for an increased understanding of the growth parameters and mechanisms of InSb nanostructures.